JPS62282205A - Measuring method of shape error of article and its apparatus - Google Patents

Abstract

PURPOSE:To simplify operation for measurement, by minimizing deviation from interference fringes by allowing a beam of reference light to deviate successively from a beam of light of a specimen article by a phase phi and adjusting a posture, etc. of the specimen article basing upon moire-image interference fringes of imaginary and actual beams of interference light. CONSTITUTION:A laser beam irradiates a aspherical mirror 16 and reference mirror 12 through an interferometer 3 and each reflected light is irradiated onto an image sensor monitor 11 for making interference fringes. Next, an arithmetic operation circuit 21 calculates imaginary interference fringes at the time when the specimen article is in the ideal situation and the imaginary reference beam is shifted from the imaginary article light by N-stage phi and store them. These imaginary interference fringes are read out successively 23 and the reference beam 7, in synchronization with above, is allowed to shift from the article light 6 by N-stage phi(x, y) [position on the position coordinates (X, Y) plane at center of the image] and sum, difference, product and quotient of actual and imaginary interference fringes by each beams of light obtained by each displacement are put into arithmetic operations 15. Basing upon these data, position, posture of the mirror 16 are adjusted 18, 19. Finally, arithmetic operation is conducted on phi(X, Y) and by utilizing a linear relation between phi(X, Y) and shape error, the shape error of the mirror 16 is obtained.

Description

Detailed Description of the Invention [Object of the Invention] (Industrial Application Field) The present invention relates to a method and apparatus for measuring all shape errors of an object.

(Prior art) In measuring the error (shape error) of a three-dimensional object that has a complex shape but is optically smooth and can be expressed by a mathematical formula, with respect to a predetermined ideal shape to be formed. , the interference fringes are formed by interfering the object beam and the reference beam, and the phase difference between the object beam and the reference beam is changed. Based on the linear relationship between the phase difference and the shape error, the interference fringes are formed. A method has been proposed in which the shape error of the object to be measured is determined by calculating the intensity distribution of the object (Japanese Patent Application No. 61-69950). According to this method, highly accurate measurement is possible without the intensity distribution of interference fringes deviating from the sine distribution. It is not necessary to create a hologram, and the workability is good.

ZARANIMA9: Emit coherent light, and make the reflected light of the coherent light as the reference light from the reference object interfere with the reflected light of the coherent light as the object light from the measured object. Obtain interference fringes, measure the phase difference of the side skin emitted light from the obtained interference fringes,
A method has also been proposed in which the shape value of the object to be measured is determined from the phase difference, and the shape error of the object to be measured is determined from the shape value (Japanese Patent Application No. 61-69951). This measurement method also does not require the creation of a hologram, so it is highly workable, and it is possible to obtain highly accurate measurement results without being affected by shadows caused by the deviation of the intensity distribution of interference fringes from the sine distribution. 9 measurements can be performed very easily.

(Problem to be solved by the invention) The following measurement method, which makes full use of the linear relationship between the phase difference and the shape error, has high accuracy, but if there is a large deviation in posture or position between the measured object and the virtual object, it may appear Errors occur, and the correction calculation requires a large amount of time. In addition, the method of measuring errors from shape values is easy to measure, but the measurement accuracy is not high enough, and the measurement range is also relatively narrow, making it difficult to measure the shape errors of deep aspheric surfaces. O [Construction of the Invention (Initial Means and Effects for Determining Problems) This invention was made in view of the above circumstances, and its purpose is to simplify the calculation following shape error measurement. A method and device for measuring the shape error of an object that can be processed in a short time and can measure with high precision even for objects with a deep depth. The method of measuring shape errors of the invention stores virtual interference fringes of a virtual ideal object to be measured;
In synchronization with the readout of the stored virtual interference fringes, the reference light is sequentially shifted by the phase ψ(xpy) from the measured object light to minimize the difference between the virtual interference light and the actual interference light. The attitude or position of the object to be measured is fully adjusted based on the moiré fringes, and in this state, the actual intensity distribution of the interference fringes is determined to measure the shape error.

Further, the device of the present invention for measuring all shape errors of an object has the following features:
means for storing virtual interference fringes of a virtual ideal object to be measured; means for reading out all terms of the virtual interference fringes from the storage means; The apparatus is equipped with a means for sequentially shifting the reference beam by an amount of ψ to determine the intensity distribution of the interference light between the object to be measured and the reference beam, and measuring the shape error from this intensity distribution.

The method of measuring the shape of an object according to the present invention allows correction calculations for deviations in the position and orientation of the object to be measured to be performed in a short time when measuring the shape error of a three-dimensional object that is optically smooth and determined by a mathematical formula. Moreover, measurement accuracy can be improved.

Further, the device for measuring the shape error of an object according to the present invention includes:
Measurement time can be shortened and measurement accuracy can be improved without making the configuration particularly complicated.

(Embodiment) A method and apparatus for measuring all shape errors of an object according to an embodiment of the present invention will be described with reference to FIGS. 1, 2A, 2B, and 3.

FIG. 1 is a diagram schematically showing a measuring device according to an embodiment of the present invention.

The operation is illustrated in the flowcharts of FIGS. 2A and 2B. To be more specific, the coherent light source 1 emits coherent light, and in this embodiment, it is a laser beam oscillator that emits radar light as a beam of light. The laser beam emitted from the laser beam oscillator I then enters a Michelinson interferometer 3 placed on its path.

The interferometer 3 includes a collimator lens e4, a semi-transparent mirror 5. It consists of a condensing lens) es and an imaging lens 10. Lede
The laser beam emitted from the optical oscillator 1 and incident on the collimator lens 4 is expanded into a parallel beam. A semi-transparent mirror 5 is arranged at an angle of about 45 degrees on the path of the next laser beam, and the parallel laser beam is incident on the semi-transparent mirror 5. The semi-transparent mirror 5 divides the incident parallel laser light sound into a deflected laser light that travels in a direction perpendicular to the direction in which it has traveled, and a straight laser light that travels directly in the direction of the hole.

The polarized laser beam enters an aspherical mirror 16, which is an object to be measured, which is placed in front of the polarized laser beam through a condenser lens 8t, which is placed in the direction in which the polarized laser beam travels.
reflect. This reflected light is passed through the condensing lens 8 as object light 6.
The parallel light beams are turned back into parallel light beams, passed through a semi-transparent mirror 5t, and then directed to an image sensor monitor (hereinafter referred to as a sensor monitor) 11 via an imaging lens 10f disposed on the path of the parallel light beams. On the other hand, collimator lens 4
The laser beam that enters the semi-transparent mirror 5 via the semi-transparent mirror 5 and travels straight through the semi-transparent mirror 5 enters a reference mirror 12 as a reference body disposed in the direction of movement of the laser beam, and is reflected. The reflected laser beam is returned to the semi-transparent mirror 7 as a reference beam, that is, a reference beam 7, and is deflected by the semi-transparent mirror 7 to the imaging lens 10t.
- to the sensor monitor 11 via. Condensing lens 8
is intended to deflect the laser beam incident thereon so that it is incident perpendicularly to the aspherical mirror 16. The imaging lens 10 completely deflects the object light 6 and the reference light 7 and directs them toward the imaging surface of the sensor monitor 11 . The object light 6 and the reference light 7 interfere with each other by the interferometer 3, and therefore, on the image plane of the sensor monitor 11, interference fringes 3 as shown in FIG.
2 is hail.

The aspherical mirror 16 is held in place by a holder 17, while the aspherical mirror 16 is attached to the holder 17 and a screw member 18 is attached to the holder 17.
．． 19, its position and posture can be adjusted. Although this embodiment is an example in which the present invention is applied to an object to be measured consisting of an aspherical mirror 16, it is naturally applicable to the case where the object to be measured is a plane mirror. In this case, the condenser lens 8 is not necessary. In that case, the laser beam enters the semi-transparent @5 via the collimator lens 4, is deflected by the semi-transparent mirror 5, and is directed to the plane mirror. It will return to 5.

In the apparatus shown in FIG. 1, a driver 1 is provided below the reference mirror 12.
3 is provided, and the phase of the reference light 2 is changed by driving this drive device 13 to move the entire reference mirror 12 finely. Accordingly, the interference fringes also change. In this embodiment, due to the movement of the driver 13, the phase of the reference light 70 is ψ
It changes by π/2 in N steps.

In this embodiment, an arithmetic circuit 21 is provided.

The arithmetic circuit 21 generates an image of interference fringes that is assumed to be imaged on the display screen of the sensor monitor 11 when it is assumed that the aspherical mirror 16 is Rie-like and has no shape error. Calculate the signal.

This calculated video signal is sent to a video device such as a TV monitor 2.
4, virtual interference fringes 32 as shown in FIG. 13 will be imaged. Arithmetic circuit 2
1 further calculates the virtual interference fringe in the following case by changing the phase of the reference beam 7 by ψ in N steps, and the calculated virtual interference fringe is
The information is input to and stored in a storage device 22 having two storage units.

A readout circuit 23 is further provided, and this readout circuit 23 reads signals of different phases from the N storage units in synchronization with the drive of the driver 13 according to the control signal from the 1-drive controller 14. Video signals of N virtual interference fringes are read out in order. The drive controller 14 outputs a control signal for controlling all driving of the drive device 13, and outputs a readout signal to the readout circuit in synchronization with the control signal. A video signal of virtual interference fringes read out by the succession circuit 23 in response to a readout signal from the drive controller 14 is input to a memory processor (hereinafter referred to as a memory processor) 15.

The memory processor 15 receives the virtual interference fringe image signal from the storage device 22 and the actual interference fringe image signal of the aspherical mirror 16 from the sensor monitor 11, and processes the sum, product, difference, or product of both image signals. Calculate. By the way, the reason for doing this calculation is that the object to be measured is an aspherical mirror 16.
Since the interference fringes in this case are very dense, this is done in order to reduce the density by integrating the interference fringes within a pixel.

The results calculated by the memory processor 15 are input to a video device, for example a TV monitor 24. in this case,
Moire fringes 33, which are the actual interference fringes and the virtual interference fringes, are imaged on the display screen. If there is no shape error in the aspherical mirror 16 that is the object to be measured, the moire fringes 33 will not appear or the adjustment screw member 18 provided on the holder 17 will not appear.
．． By adjusting the position and orientation of the aspherical mirror 16 using 19, it can be made into a straight line. When including shape errors, it always becomes a curve. Then, as mentioned above, the reference light 7
By changing the phase in N steps (N is an integer of 2 or more), only the moiré fringes appear clearly.

By the way, a TV monitor normally displays 30 screens per second. Therefore, when N is 3 or 4 and 2π ψ is K, the clearest moire fringes can be obtained.

If the memory processor outputs an average of several levels of moire fringes, the moire fringes will become even clearer. In this request: 1. Drive the drive device 13f and refer to ml 2'
! i- By making a minute movement, the phase of the reference beam 7 is completely changed. The drive controller I4 adjusts the phase difference ψ(X, Y
) in four stages of π/2, that is, ψ(X+7)+ψ
(X+7)7ψ(x,y)+π.

The driving device 13 is arranged so that the change occurs in four stages: ψ(X, Y) 10÷π. The memory processor 15 is provided between the sensor monitor 11 and the drive controller 14, and generates interference fringes on the sensor monitor 11 in synchronization with each four-step change in the phase of the reference light 7 caused by the drive controller I4. It receives video images, converts them into digital signals, and stores them. By the way, when the phase of the reference light 70 is changed in four stages, the arithmetic circuit 15
The intensity distribution of the interference fringes input to is I N (x+y)−τ. (X,Y)C1+γcos
(W (X, Y) + ψb, y) ” 2 (N1) )
) (x).

Here, r N (x ry ) is the intensity distribution of the interference fringe on the image plane, that is, on the X, Y coordinate plane, at the Nth change stage, and r o (" + y ) is the intensity distribution of the radar light itself. The intensity distribution, T, (bias component of (X, Y), γ is the clarity of the interference fringe, ψCx, y) is the phase distribution (unit: N is an ordinal number indicating the stage of change in the phase of the reference light 70, and is an integer from 1 to 4. In the above equation (1), W (X, Y)
shows the phase distribution of the object beam 6 when the shape error of the aspherical mirror 16, which is the object to be measured, is zero;
It can be calculated more easily than the design value.

The size t of one pixel on the image plane consisting of the x, y coordinate plane,
Breath in the x direction, b in the Y direction, coordinate position of the center of the pixel (X,
Y), the brightness intensity EN(X,
Y) is given by. Here, f(x-X, y-Y) is a function giving the shape of one pixel and the photosensitivity distribution. In addition, (X,
Y) is the coordinate of the center position of the pixel, and (X, y) is the coordinate of an arbitrary position on the X, Y coordinate plane. As the sensor monitor 11, an ITV camera, a CCD play camera, an image dissector camera, or a photo array sensor ring can be used. In the case of a CCD array camera or photoarray sensor,
Since the photosensitivity is uniform over the entire area of the photosensitive surface and the pixel shape is rectangular, f(x
-X, y-Y) terms have no substantial effect even if they are omitted.

Substituting equation (1) into equation (2) and expanding it, we find that the size of one pixel is generally several 10
The intensity distribution I(X, Y) of the secondary laser beam itself is sufficiently small as 1/0, and the phase distribution 9'(x,
y) changes slowly. Next, within one pixel, ro(X, Y).

ψ(X, Y) is considered to be uniform and can be excluded from the above equation (3). That is, if we define here, equation (4) can be written as the following equation (6).

+C(X,Y)・r(X,Y)・γ・go(ψ(X,Y
)+u(N-1))-s(X,Y)-r(X,Y)・
r-ground (91'(X, Y)+H(N-1)) where N-
When 1. (ψ(x, 7)+1(N-1)) −cmψ(x, y
) = (9'(X, Y) (N1)) - ginψ(X,
Y)・N-2, m(9'(X, Y)+-2(N-1)) -coi[ψ
(X, Y) + 7) ff1-dnψ(x, y) (ψ(
X, Y)←(N-1)) =m(ψ(X+7)+7)
-(fflψ(X+7)・N When 3) (ψ(X, Y)+100(N-1))-Residence(ψ(X, Y
) 1π) - Partial ψ(X, Y) sin(ψ(X, Y) + H
(N-1)) -5i(ψ(X,Y)+yr) =-a
When ψ(X, Y)・N=4, Cx1s(ψ(X, Y)+-2(N-1))=CIlI
S(ψ(” + y) +Σπ) = slnψ(S,
y) 廁(ψ(X,Y)←(N 1)) −5in(ψ(
X, Y) + Lr) −-amψ(X, Y) Using equations (6) and (7) to calculate EA = E, (XIY) - E3 (X, Y), EA Tomoe E1 (X, Y)-E3(X,Y)=21o(
X, Y)r(C(X,Y)casψ(X,Y)-8(X
, Y)th9'(X, Y)) (8). Similarly, using equations (6) and (7), E, -E4(X,Y)-
E2 (X, Y) After all calculations, E, -E14 (X, Y)
-P22(X,Y)=2r,(X,Y)r(C
(X, Y) gh 9' (X, Y)+s (X, Y)
as 9) (X, Y) ) (9) Equation (8) and Equation (9)
From α1, the desired ψ(X, Y) can be obtained using the following formula.

To summarize the above, the object light 50 phase distribution ψ(X, Y) caused by the shape error can be found by the following calculation procedure (second
Figure B).

(2) Assuming that the aspherical mirror 16 of the object to be measured and the soldering iron have no shape errors, obtain a virtual phase distribution w (x + y) of the companion object light 6 reflected by the aspherical mirror 16 with a design shape.

■ Equation (5) All operations are performed to calculate c (x,
y) and s(X, Y).

■　α＊　,　(11)The following formula 9 formula %) Perform all calculations to find ψ(X, Y).

Even if we calculate E' (X, Y) - E (X, Y), we obtain the same result as the formula αQ. Unfortunately, the calculations are complicated.

In the round hole (1), j+Xj7) -1o(X, Y)D+γQl! l (W
(x,y)+ψ(X,Y)+1(N-1))](1-a
) The same thing can be done by changing the phase in three steps.

In this case, equation (3) is I x
Even if you calculate with If, you will get the same result as E"(X, Y) = E(X, Y), which is the same as the formula α1. At this time, the change in phase ￥
'i3 steps are sufficient, but the calculation becomes complicated as in equation (101K).

Next, consider a situation where the position or orientation of an object is shifted. Here, this deviation i! 'f-x, ΔX, Δ in the y direction
y, a coefficient of distortion in the phase of the object light 60 due to deviation in the optical axis direction (two directions), total α, and a coefficient iT1 of distortion in the phase of the object light 6 due to the tilt of the y-axis ゎυ. Similarly, let T2 be that around the X axis. Object light 6 due to position and orientation deviation that integrates the above
Let we (x*y) be the distribution of phase distortion of , and it can be expressed by the following equation.

W2 (X, Y) = α・((x−ΔXzo+(y−7fy
)2) +71・(x−Δx)+T2・(y−Δy
) At this time, the intensity distribution rN(''+7) of the interference fringes is expressed by the formula (
1) % formula %() where formula (4) , (5) , (6) , (8)
After doing some calculations, the formula (1Q is written as
The operation to obtain tan g(X, Y) is aretmnE
(X, Y) III W, (X, Y) + 911 (X
−Δx+Y−Δy) It is written as α伜. 2 αQ is the object light 60 phase distortion due to the position and orientation of the object w
, (X, Y) contains y and b, so this w, (
An accurate shape error cannot be obtained unless the values (X, Y) are removed. To make sure of this, the standard deviation of ar@tan E (X+Y) over all pixels, ie.

The above-mentioned holder I7 is attached to the interferometer 3 so that
If the position and orientation of the aspherical mirror 16 are adjusted relative to each other by rotating the screw members 11J and 19't provided in the Since it does not change and remains constant, from the formula (IQ), it can be considered that W, (X, Y) ~ O across all pixels.In this case, formula %Q, T, = + = O, T2-0 So, the formula αQ is a
rctxn E(X, Y)-ψ(X, Y), and by substituting this price into the equation λ H(X, )l)-ψb, y) x −+ K, the shape error H(X, Y) is found.

By the way, when a one-dimensional sensor, such as a Funado array sensor, is used as the sensor monitor I, the number of pixels is small and the calculation time is short, but when a two-dimensional sensor is used, the number of pixels is large, and the process of calculation → adjustment operation → calculation →You will have to repeatedly operate the screws, which takes a lot of time. At this time, the above five non-rammeters α, ΔX are calculated by calculation.
,ΔyIT! IT2 is completely calculated to find w, (X, Y), and finally ψ(X, Y) can be obtained.

By the way, it is difficult to obtain the above five parameters at the same time by calculation within the arithmetic unit, so this 51/4' parameter? The steps to divide and calculate in order are shown below.

To simplify the calculation, we utilize the fact that the α term is of even order, the others are of odd order, T1 is a term only for x@J3, and T2 is a term only for the y-axis. First, we determine T1 and ΔX. Considering only the X axis, 2α9 is We (x r o
)-α・(e-Δx)2×T1・(x-ΔX)
It will be day α. Here, Δx * T1's expected compensation Δxl'
,T,', then the next performance 'J!' to delete the even numbered tops! !
, all done.

g(X+lx'lT1') = aretmnE(X+
Δx', 0)-arctin E(-X+Δx'+0
)-271'-X (Substituting the formula α→, α1 into d2〇电 gives g(X, Δx/ , T, /) the value α-((X-ΔX+Δx')-(-X-Δχ+ΔX
')) 10T, ・((X-Δχ+Δ!')-(-X-Δx
+lx') )+ψ(X-ΔX+Δ3ψ(-x-Δ
χ+ΔxQ 2T+' ・X==4α・X(ΔxlΔ
x ) + 2X ・(T 1T 1' ) + ψ(X-
ΔX+Δx/) ~ ψ(-X−Δχ+Δx/)
According to Kan formula (1), Δχ−Δx', T, w T
, ', then g(X, Δx/, T17) - ψ(X-Δx+x Lee ψ(-X-ΔX+Δx'), and g(X, Δx/, T, / Standard deviation σ2d・
indicates the minimum value. Conversely, Δx that minimizes σgX
You can find it in 'aT+'. Since there are only two parameters, it can be easily determined using a general trial-and-error method.

Similarly, for the Y-axis, g (Y, Δy'+T2') total calculation (78σ, find Δy' and T2' such that a is minimized. Through the above, 4 out of 5 parameters are found, and the remaining 1 piece.To find this, we have calculated the following Δ
From x/, Δy', T,', T2', Δ8−Δ
xl, ΔAΔY' pT, -* T1'・T0n
By substituting T2' into equation (6) ~ α, the value of α that minimizes σ can be found. As a result, all five mother meters are found υ, and by substituting these values into equations (g) to α9, we get the value of arctan E(X, Y) and w, (
The value of ψ(X-Δx, Y
-Δy) is found, and the shape error 4π H(x-dx, y-ΔX) is obtained by H(x-Δx, y-Δx)=λ ψ(X-ΔX+7-Δy)X−+.

As in this example, when the object is an aspherical mirror, there is no practical problem even if the focal length of the aspherical mirror is slightly different from the design value as long as it is within the tolerance.
It is measured as an apparent shape error.

Therefore, when the parameter β related to the focal length shift is set, equation (a) becomes w, (X, Y) - α・((X-dx)2+(y-Δy)
2)+β((X-dx)2+(y-Δy)2)2+T
The gradient is 1.(x-dx) + T2.(y-Δy). β・((e−dx) +(y−Δy)) is also an even function, so as mentioned above, ΔF, ΔF+TI+T2'
After estimating i, α and β may be found simultaneously so that the σ-factor is minimized.

From the above, the shape error can be found.

According to the measuring method and measuring device of the above embodiments, even if an object has a complex shape, if it can be formed using an aspherical equation and is optically smooth, the shape error can be calculated easily and easily. It is possible to measure with high precision, and even if a sensor monitor with a small number of pixels is used, the measurement can be performed with high precision.

In this embodiment, the phase of the reference light 7 must be changed accurately by 100 degrees, and a method of calibration will be described below. If this calibration is not completed and the phase of the reference beam 7 is
), then equation (1) becomes rN (X, Y) ” ■o (X, Y) C” + γc
ts (W (X, Y) + 'i' (x + y) + Shima + ε)
(N-1)) ■. If we substitute the formula (goods) into formula (3), we get EN(
X, Y) is +f(X-X, y-Y) ・γ・tyys (W(X,
Y) + ψ (X, Y) + (-+ε) (N-1)) dXdy
(c) Like N Plastic Oke Challenge 11
Since ε4Q is here, −εxg+sm2ε=2ε.

If blood 3g cod 3εrcage part υ1 house 3ε = 1 -
2gccs(W(X,Y)+ψ(X,Y))+ψ(X,
Y) ←) dxdy (c).

From equation (c), if the phase of the reference beam 7 is accurately displaced by i, then ε-0 and D will also be zero.

In other words, the position of the reference beam 7 may be adjusted by fully adjusting the drive device 13 using the motion controller 14 so that all pixels are set to D-0.

Note that this invention is not limited to the above embodiments. For example, in this embodiment, the measurement method of the invention is applied to nine aspherical mirrors as the object to be measured, but the surface is not limited to this, and the surface is smooth against the light source used, and the measurement method is It can be applied to all objects whose shape can be expressed.

At this time, the calculation procedure from equation (1) to 2α7) is the same.

As the light source, any light source can be used as long as it emits coherent light, although we will use it as an example of laser light and sound. Examples include infrared laser light or near-ultraviolet light from a mercury lamp.

A Michelson type interferometer was used as the interferometer, but any interferometer can be used as long as it measures the entire shape of an optically smooth surface.

Examples include the Mach-Zehnder interferometer and the Fizeau interferometer.

Seven thermal monitors include ITV, storage type image sensors such as CCD sensors, and photo array sensors.

Although there are other types such as image dissectors, shape errors are determined using the same calculation procedure.

When using a linear array sensor, a -axis cross-sectional shape can be obtained.

Further, in the above embodiment, the phase of the reference light is shifted one by one in all steps, but it may be changed continuously and data may be captured instantaneously at -9 timings.

It is not necessary to input data instantaneously for all images at the same time, and it is also possible to input all data one pixel at a time. In this case, the phase of the reference light differs slightly from pixel to pixel, and this can be taken into consideration and subtracted from the shape measurement data.

In this embodiment, the phase of the reference light was completely changed.

The same effect can be obtained by providing the drive device 13 on the aspherical mirror 16 that is the object to be measured and changing the phase of the object light 6.

In this embodiment, the light reflected on the surface of the aspherical mirror I6 is used as the object light 6, but if the object is transparent, the light completely transmitted through the object may be used as the object light.

[Effects of the Invention] In measuring the shape error of an object to be measured, the process that requires the most time is the calculation for correcting the deviation in the posture and position of the object to be measured. As is clear, the measurement processing time can be greatly shortened without complicating the configuration, and shape errors can be measured with high accuracy.

[Brief explanation of the drawing]

FIG. 1 is a diagram illustrating the entire configuration of a device for measuring shape errors according to a practical example of the present invention; FIGS. 2A and 2B are operational flowcharts of a measuring method carried out with the device shown in FIG. 1; FIG. 3 is a diagram showing all the moiré fringes caused by interference between the object light and the reference light. DESCRIPTION OF SYMBOLS 1...Laser light source, 3...Interferometer, 5...Semi-transparent mirror, 8...Condenser lens, 10...Imaging lens, 11
...Image-sensor monitor, 12...Reference mirror,
13... Drive device, 14... Drive controller, 15...
・Memory data processor, 21... Arithmetic circuit,
22...Storage device, 23...Reading circuit, 24...
・1"V monitor. Applicant's representative Patent attorney Takehiko Suzue Figure 2A Figure 2B Figure 3

Claims (25)

[Claims] (1) (a) Emit coherent light; (b) cause the reflected light of the coherent light as a reference light from a reference object and the reflected light as object light from a measured object to interfere; Obtain actual interference fringes, (c) change the phase difference between the object beam and the reference beam in N steps by ψ(x, y) and store the actual image signal at each step; (d) It is assumed that the object to be measured has an ideal design shape value, and the phase difference between the virtual object light and the virtual reference light is changed in N steps by ψ (x, y). (e) determining a shape error of the object to be measured based on the actual interference fringes and the virtual interference fringes, the method comprising: The procedure (e) above includes: storing a virtual video signal at each stage of the N stages of phase difference change when determining the virtual interference fringe, sequentially reading out the stored virtual video signal at each stage, and reading out the sequential reading. The phase difference ψ(χ, y) between the object light and the reference light is relatively changed in synchronization with ψ(x, y), ψ(x, y). y)+π/
2. The intensity distribution of the interference light in the interference fringes obtained by varying ψ(x, y) + π and ψ(x, y) + 3/2π on the X and Y coordinates, and the intensities E_1 (X, Y) and E_2 (X
, Y), E_3(X, Y), E_4(X, Y), and the phase distribution W(x, y) of the coherent light reflected from the object to be measured assuming that there is no shape error. is calculated based on the design value of the shape of the object to be measured, and (X, Y)
The sensitivity distribution at the pixel at the coordinate position is f(x-X, y-Y
), and the size of the pixel is a in the x direction and b in the y direction, then ▲ There are mathematical formulas, chemical formulas, tables, etc. ▼ ▲ There are mathematical formulas, chemical formulas, tables, etc. ▼ Calculate E(X, Y) As the tangent value, calculate ▲ There are mathematical formulas, chemical formulas, tables, etc. ▼ and ▲ There are mathematical formulas, chemical formulas, tables, etc. ▼ and calculate the phase difference ψ (
X, Y), and the phase difference ψ(X, Y) and the (X
, Y) A method for measuring a shape error of an object, characterized in that the shape error of the object to be measured is calculated based on a linear relationship between the shape error of the object to be measured at the coordinate position. (2) Let the numbers of pixels in the x direction and y direction of the X and Y coordinates be m and n, respectively, let the coordinate positions of the center of the i-th pixel in the x direction and the j-th pixel in the Y direction be X_i and Y_j, and the tangent of the pixel When the value is E(X_i, Y_j), arctan{
E(X_i, Y_j)}, the standard deviation σ_E, ▲There are mathematical formulas, chemical formulas, tables, etc.▼ is calculated, and the relative position and/or orientation of the object to be measured and the interferometer is calculated so that σ_E takes the minimum value. 2. The method for measuring an object shape error according to claim 1, wherein the method comprises adjusting the deviation of the object shape. (3) The amount of deviation in the relative position and/or posture is
Δx in the direction, Δy in the Y direction, Δz in the Z direction, T_1 in the y-axis rotation angle direction, T_2 in the x-axis rotation angle direction, and T_3 in the z-axis rotation angle direction, and refer to the object light according to these deviation amounts. Let the contribution to the phase difference of light be W_e(x, y), and Δx
, Δy, Δz, T_1, T_2, T_3, and the above Δ
W_e (x, y) is calculated from the obtained values of x, Δy, Δz, T_1, T_2, T_3, and (X
, Y) When the intensity of the brightness of the pixel whose coordinate position is the center coordinate position is E(X, Y), arctan{E(X,
Subtract W_e(X, Y) from ψ(X, Y)
The operation to find ψ(X, Y)=arctan{E(X,
3. The method for measuring a shape error of an object according to claim 2, characterized in that: Y)}-W_e(X, Y). (4) ψ(X,Y)=arctan{E(X,Y)}-
Instead of W_e (X, Y), ▲ There are mathematical formulas, chemical formulas, tables, etc. ▼ ▲ There are mathematical formulas, chemical formulas, tables, etc. ▼ E' (X, Y) = {C' (X, Y) [E_4 (X , Y)
-E_2(X,Y)]-S'[E_1(X,Y)-E_
3(X, Y)]}/{C'(X, Y)[E_1(X, Y
)-E_3(X,Y)]+S'[E_4(X,Y)-E
_3(X, Y)]} The method for measuring a shape error of an object according to claim 3, characterized in that the difference is calculated. (5) Estimated values Δx', Δy of these six values as a procedure for calculating Δx, Δy, Δz, T_1, T_2, T_3
′, Δz′, T_1′, T_2′, T_3′,
While changing these estimated values, calculate the estimated value W_e'(X, Y) of W_e(X, Y), and calculate W_e'(X, Y).
Substitute W_e(X, Y), calculate ▲There are mathematical formulas, chemical formulas, tables, etc.▼, and calculate Δx′, Δy when σ′_E has the minimum value.
', Δz', T_1', T_2', T_3' are obtained as values equal to the above-mentioned Δx, Δy, Δz, T_1, T_2, T_3, the object according to claim 3. How to measure the shape error of. (6) When the object to be measured is an optical element having a rotating aspherical surface, Δx, Δy, Δz, T_1, T
6. The method of measuring the shape error of an object according to claim 5, characterized in that the step of determining T_3 is excluded from the steps of determining T_3. (7) Instead of the above procedure for calculating Δz, the coefficient α of the distortion of the object light phase due to Δz is taken as the coefficient α, and a procedure for calculating α is provided, W_e(x,y)=α・{(x−Δx)＾2+( y-Δ
y)^2}+T_1・(x-Δx)+T_2・(y-Δ
7. The method for measuring a shape error of an object according to claim 6, characterized in that W_e(x, y) is determined by calculating W_e(x, y). (8) Add a procedure to find the coefficient β of the phase distortion of the object light due to the amount of focal length deviation of the optical element with a rotating aspherical surface, and calculate W_e(x,y)=α・{(x−Δx) ^2+(y-Δ
y)^2}+β・{(x-Δx)^2+(y-Δy)^
2}^2+T_1・(x-Δx)+T_2(y-Δy)
8. A method for measuring a shape error of an object according to claim 7, characterized in that W_e(x, y) is determined by the following calculation. (9) As a procedure for finding α, β, Δx, Δy, T_1, and T_2, first consider the x-axis, and calculate W_e(x, o)=α・(x−Δx)^2+β・(x−
Δx)^4+T_1(x-Δx), the estimated values of Δx and T_1 are Δx', T_1', and for the pixel at the coordinate value of (X, o), g(X, Δx', T_1') = arctanE' (X+
Δx′,o)−arctanE′(−X+Δx′,o)
-2T_1'・X and g(X, Δx', T_1') are defined, and while changing Δx' and T_1', g(X, Δx',
Calculate the standard deviation σ_g_X of T_1', that is, ▲There are mathematical formulas, chemical formulas, tables, etc.▼, and calculate the values of Δx' and T_1' when σ_g_X has the minimum value.
Second, considering the y-axis, W_e(o, y)=α・(y−Δy)^2+β・(y−
Δy)^4+T_2(y-Δy), and the estimated values of Δy and T_2 are Δy'・T_2', and for the pixel at the coordinates of (o, Y), g(Y, Δy', T_2') = arctanE'( Y+
Δy', o)-arctanE'(-Y+-y', o)
-2T_2'Y and g(Y, Δy', T_2') are defined, and while changing Δy' and T_2', g(Y, Δy',
T_2′) standard deviation σ_g_Y is calculated, and σ_g_Y
A procedure for determining that the values of Δy' and T_2' when Δy' and T_2' have the minimum value are equal to the values of Δy and T_2, and thirdly, the obtained Δx, Δy, T_1, and T_2 are defined in claim 8. Substitute into the operation of W_e (x, y) described in the section,
E'(X, Y) as set forth in claim 4 is calculated while changing the values of α and β in W_e(x, y), and σ_E' as set forth in claim 5 is calculated. Calculate σ_E′
α and β are calculated using the values of α and β when has the minimum value.
Claim 8, characterized in that it comprises means for setting the value to .
A method for measuring the shape error of an object as described in Section. (10) When calculating the standard deviation, σ_E and σ_E' are for all pixels, and σ_g_X and σ_g_Y are x
Claims 2 and 5 are characterized in that instead of calculating the standard deviation for all pixels on the axis and the y-axis, the standard deviation is calculated only for a plurality of specific pixels.
10. A method for measuring a shape error of an object according to any one of Items 1 and 9. (11) When the sensitivity within a pixel is uniform, f(x-X, y-
A method for measuring a shape error of an object according to any one of claims 1 to 10, characterized in that X)=constant. (12) When the pixel sizes a and b are sufficiently small, C(X
, Y)=cosW(x,y) S(X,Y)=sinW(x,y) according to any one of claims 1 to 11. , a method for measuring shape errors of objects. (13) (a) means for emitting coherent light; (b) reference body means; (c) reflected light of the coherent light as reference light from the reference body means and from the object to be measured; (d) means for providing actual interference fringes of both the reflected lights; and (e) means for causing the measured object to have an ideal design shape value. (f) calculating means for calculating virtual interference fringes when the phase difference between the virtual object light from the virtual object and the virtual reference light is changed in N steps by ψ(x, y); storage means for storing virtual image signals of each of the N stages of the virtual interference fringes obtained by the calculation means; (g) reading means for sequentially reading out the virtual image signals of each stage from the storage means; (h) driving means for driving the reference body means and thereby changing the phase of the reflected light from the reference body means; The phase difference ψ(x,
y), and the phase difference ψ(x, y) is changed to ψ
(x, y), ψ(x, y)+π/2, ψ(x, y)+π
, ψ(x, y) + 3/2π, respectively, on the X and Y coordinate planes, the intensity distributions of the interference light are expressed as intensities E_1 (X, Y), E_2 (X, Y), E_3 (X,
Y), E_4(X, Y), and the phase distribution W(x, y) of the virtual object light reflected from the object to be measured when there is no shape error based on the design value of the shape of the object to be measured.
), the sensitivity distribution at the pixel at the (X, Y) coordinate position is f(x-X, y-Y), and the pixel size is a in the x direction.
, when b is in the y direction, ▲There are mathematical formulas, chemical formulas, tables, etc.▼ Calculate, E(X, Y) is the tangent value, ▲There are mathematical formulas, chemical formulas, tables, etc.▼ and ▲Mathematical formulas, chemical formulas, There is a table etc. ▼ Calculate the phase difference ψ at the above (X, Y) coordinate position.
(X, Y), and the phase difference ψ(X, Y) and the (X, Y) are calculated.
means for calculating the shape error of the object to be measured based on the fact that there is a linear relationship between the shape error of the object to be measured at the (X, Y) coordinate position. A device that measures errors. (14) An apparatus for measuring a shape error of an object according to claim 13, wherein the means for providing the interference fringes is an ITV camera. (15) The device for measuring the shape error of an object according to claim 13, wherein the means for providing the interference fringes is a camera having a solid-state image sensor. (16) The apparatus for measuring shape errors of an object according to claim 13, wherein the means for providing the interference fringes is an image dissector camera. (17) An apparatus for measuring a shape error of an object according to claim 13, wherein the means for providing the interferometer is a photoarray sensor. (18) Claim 13, wherein the means for emitting coherent light is a visible laser beam oscillator.
A device for measuring the shape error of an object, as described in . (19) Claim 13, wherein the means for emitting coherent light is an infrared laser beam oscillator.
A device for measuring the shape error of an object, as described in . (20) The interference device according to claim 13, wherein the interference means is a Mach-Zehnder interferometer.
A device that measures the shape error of objects. (21) Measuring the shape error of an object according to claim 13, wherein the interference means is a mirror with a highly accurate shape disposed on the back surface of the object to be measured. Device. (22) An apparatus for measuring a shape error of an object according to claim 13, wherein the interference means is a Michelson interferometer. (23) An apparatus for measuring a shape error of an object according to claim 13, wherein the interference means is a Fizeau type interferometer. (24) An apparatus for measuring a shape error of an object according to claim 13, further comprising means for holding the object to be measured and adjusting its position and/or posture. . (25) The apparatus for measuring a shape error of an object according to claim 13, wherein the means for providing the interference fringes is an ITV camera.